The Gradient That Top-k Distillation Never Computes
Many deployed distillation pipelines show the student a truncated view of the teacher: keep the top-k probabilities, renormalize, and minimize a divergence on what remains. Renormalization is assumed to account for the missing mass. We prove that it removes the visibility of tail mass, not the freedom to move it. The renormalized objective depends only on log-odds among the retained tokens, so at each position its gradient along the directions that control tail mass is exactly zero; on a real teacher that component measures $2$-$3\times10^{-15}$ of the gradient. The full-vocabulary gradient equals the truncated gradient plus a residual weighted by the tail masses, and training acts only o...
| Authors | Rasul Khanbayov, Hasan Kurban |
|---|---|
| Primary category | cs.LG |
| Published | 11 October 2026 |
| Last updated at source | 11 October 2026 |
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